For example the energy (per volume) in the CMB is something we can find by raising T to the fourth and multiplying by a = pi^{2}/15
The energy of an average CMB photon is 2.701kT and since the temperature is 1.93E32 and k=1, the average energy is just
5.2E32.
the energy density aT^{4} is just 9.13E128
dividing by the average quantum energy gives the number of CMB photons per unit volume in space 1.7E96
If we want to see this for a large volume, a cubic mile for instance is E114. So the number of CMB quanta in a cubic mile has to be
1.7E18
Just to mull this over a bit: there are 1.7 billion billion CMB photons in a cubic mile and how much energy have they lost since their emission (called "recombination" or "last scattering", believed to be 300,000 years since bang.)
They were emitted at z = 1100, so they have lost all but 1/1100 of their original energy.
The current CMB energy density was just calculated to be 9.13E128. So the density of lost energy is 1100 times that:
1.004E124, essentially E124.
The energy lost from a cubic mile of CMB is E114 times that or E10two tenths of a joule. As yet no general global energy conservation theorem has been proved in General Relativity. Have to think about this two tenths of a jouledid it go anywhere or was it simply lost?
